CD meets CAT

الأصل · EN

We show that if a noncollapsed CD(K,n) space X with n≥ 2 has curvature bounded above by κ in the sense of Alexandrov then K≤ (n-1)κ and X is an Alexandrov space of curvature bounded below by K-κ(n-2). We also show that if a CD(K,n) space Y with finite n has curvature bounded above then it is infinitesimally Hilbertian.